Notes:

Summary plots - Sample strategy is on the y-axis and number of sites is on the x-axis. Each plot is paired by parameter level vertically and the values in the cells are the mean value across all of the simulations for that parameter level. Note that each average encompasses all of the other varying simulation parameters.

Full plots - Sample strategy is on the y-axis and number of sites is on the x-axis. Each plot represents a unique simulation and the values in the cells are the mean value across all of the 10 iterations of that simulation across all three unique landscape seeds (i.e., all three sets of Neutral Landscape Models) for a total of 30 replicates. For these plots: K = population size (not to be confused with the number of latent factors (K)), phi = selection strength, m = migration, H = spatial autocorrelation, r = correlation between environmental layers.

RAE - Ratio Absolute Error - is the absolute difference between the observed and expected estimate of the ratio of IBE to IBD (i.e. the coefficient of IBE divided by the coefficient of IBD)

Bias - bias was calculated by taking the mean difference between the observed and expected coefficients or ratios

1. MMRR

1.1 Individual sampling

1.1.1 Summary plots

1.1.2 Linear mixed effects models

RAE

Linear mixed effect model
statistic ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
nsamp −0.0003 8.0000 8.0000 1 15.3480K 1531.810409 1.9 × 10−319***
sampstrat 0.1078 1.5728 0.5243 3 15.3480K 100.385844 2.4 × 10−64***
K 0.0126 0.6090 0.6090 1 15.3480K 116.601181 4.4 × 10−27***
m 0.0523 10.5133 10.5133 1 15.3480K 2013.030919 0.0***
phi −0.0020 0.0155 0.0155 1 15.3480K 2.971532 0.085
H 0.0096 0.3544 0.3544 1 15.3480K 67.857541 1.9 × 10−16***
r −0.0090 0.3123 0.3123 1 15.3480K 59.800103 1.1 × 10−14***
*** p < 0.001
Tukey test
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G*** −0.0046 0.0016 −2.7960 0.02658997***
EG - R −0.0009 0.0016 −0.5319 0.95132229
EG - T** −0.0249 0.0016 −15.0697 0.0**
G - R 0.0037 0.0016 2.2641 0.10653142
G - T** −0.0202 0.0016 −12.2737 0.0**
R - T** −0.0240 0.0016 −14.5378 0.0**
*** p < 0.05
** p < 0.001

1.1.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

1.2 Site sampling

1.2.1 Summary plots

1.2.2 Linear mixed effects models

RAE

Linear mixed effect model
statistic ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
nsamp −0.0054 10.9296 10.9296 1 8.6290K 774.65997483 2.4 × 10−163***
sampstrat 0.2519 1.7532 0.8766 2 8.6290K 62.13047517 1.6 × 10−27***
K 0.0003 0.0002 0.0002 1 8.6290K 0.01177688 0.910
m 0.0196 0.8264 0.8264 1 8.6290K 58.57599989 2.2 × 10−14***
phi −0.0053 0.0618 0.0618 1 8.6290K 4.37735932 0.036**
H 0.0115 0.2873 0.2873 1 8.6290K 20.36485607 6.5 × 10−6***
r −0.0184 0.7299 0.7299 1 8.6290K 51.73067018 6.9 × 10−13***
*** p < 0.001
** p < 0.05
Tukey test
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ*** −0.0340 0.0031 −10.8514 2.7 × 10−14***
EG - R** −0.0101 0.0031 −3.2163 3.7 × 10−3**
EQ - R*** 0.0239 0.0031 7.6351 8.6 × 10−14***
*** p < 0.001
** p < 0.01

1.2.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2. GDM

2.1 Individual sampling

2.1.1 Summary plots

2.1.2 Linear mixed effects models

RAE

Linear mixed effect model
statistic ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
nsamp −0.0003 9.4335 9.4335 1 15.3430K 8.826316e+02 1.2 × 10−188***
sampstrat 0.1099 0.7896 0.2632 3 15.3430K 2.462613e+01 6.9 × 10−16***
K 0.0231 2.0533 2.0533 1 15.3430K 1.921097e+02 2.0 × 10−43***
m 0.0799 24.4973 24.4973 1 15.3430K 2.292047e+03 0.0***
phi −0.0003 0.0002 0.0002 1 15.3430K 2.244788e-02 0.88
H 0.0020 0.0153 0.0153 1 15.3430K 1.435012e+00 0.23
r −0.0057 0.1237 0.1237 1 15.3430K 1.157134e+01 6.7 × 10−4***
*** p < 0.001
Tukey test
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G*** −0.0135 0.0024 −5.7327 5.9 × 10−8***
EG - R*** −0.0097 0.0024 −4.0895 2.5 × 10−4***
EG - T*** −0.0198 0.0024 −8.3745 4.1 × 10−14***
G - R 0.0039 0.0024 1.6429 0.35443857
G - T** −0.0062 0.0024 −2.6417 0.04111055**
R - T*** −0.0101 0.0024 −4.2845 1.1 × 10−4***
*** p < 0.001
** p < 0.05

2.1.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2.1.4 Failed fits

Occasionally GDM fails to fit a model, in which case an NA value is assigned. Here we visualize the proportion of NAs (i.e., cases of failed fit) across the simulations:

Proportion of failed models:

2.2 Site sampling

2.2.1 Summary plots

2.2.2 Linear mixed effects models

RAE
Linear mixed effect model
statistic ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
nsamp −0.0064 14.4681 14.4681 1 8.3500K 5.407432e+02 5.9 × 10−116***
sampstrat 0.3179 8.3211 4.1605 2 8.3500K 1.554993e+02 5.0 × 10−67***
K 0.0000 0.0000 0.0000 1 8.3500K 2.777680e-05 1.00
m 0.0231 1.1117 1.1117 1 8.3500K 4.155104e+01 1.2 × 10−10***
phi −0.0049 0.0503 0.0503 1 8.3500K 1.879243e+00 0.17
H 0.0007 0.0009 0.0009 1 8.3500K 3.448557e-02 0.85
r −0.0137 0.3905 0.3905 1 8.3500K 1.459672e+01 1.3 × 10−4***
*** p < 0.001
Tukey test
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ*** −0.0760 0.0044 −17.3557 0.0***
EG - R*** −0.0272 0.0044 −6.1624 2.1 × 10−9***
EQ - R*** 0.0488 0.0044 11.1986 7.3 × 10−15***
*** p < 0.001

2.2.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2.2.4 Failed fits

Occasionally GDM fails to fit a model, in which case an NA value is assigned. Here we visualize the proportion of NAs (i.e., cases of failed fit) across the simulations:

Proportion of failed models: